Choose the type of capacitor that has the longest life. · Estimate the average service life of the mounting surface capacitor under normal operating conditions:
Reliability is expensive. But the cost of poor quality and reliability is even more expensive. Reliability must be supported throughout the life cycle of the product. Predicting reliability is very important for electronic components such as capacitors, diodes and resistors.
To estimate this average lifetime of the surfacemount capacitor, a specific method of acceleration of lifetime is set up. Indeed the capacitors have a life of several years, making their tests very long. Generally the acceleration of the life tests are done by accelerating the failure of the product by the addition of sustained stress.
As part of this study, two noncontrollable parameters are used: temperature and voltage. By stressing these two parameters, the life of the capacitor will be much less with reasonable failure times, and will allow an estimate of the service life under average conditions of use.
The value measured in these tests is the MTTF (Mean Time To Failure) which represents the average time of failure.
The parameters of the study are:
The mathematical model for the factors of production is the following one taking into account only the links of the second order for the factors A and B: We use the Taguchi method where we minimize the dispersion of product performance in response to noise factors while maximizing dispersion in response to signal factors. S / B ratios can be calculated using Taguchi's robust plan options. There are three ratios:
L4 full factorial design plan for production factors:
Dielectric  Production temperature  Durée de vie 
1  1  
1  2  
2  1  
2  2 
Full L8 Factorial Experiment Plan for Environmental Factors: We begin by changing the Tension factor to 4 levels by two factors at two levels:


The final experience plan is:
Tension 1  Tension 2  Température  Lifetime 
1  1  175  
1  1  190  
1  2  175  
1  2  190  
2  1  175  
2  1  190  
2  2  175  
2  2  190 
L4 + L8 Full Experience Plan Data
Tension

1

1

2

2

3

3

4

4

Signal / Bruit


Température de fonction

1

2

1

2

1

2

1

2


Diélectrique

Température de production

Moyenne

Ecart type

Maximisation

Valeur cible


1

1

430

950

560

210

310

230

250

230

396,25

2545

49,2

3,85

1

2

1080

1060

890

450

430

320

340

430

625

326,8

53,3

5,63

2

1

890

1060

680

310

310

310

250

230

505

325,5

50,5

3,8

2

2

1100

1080

1080

460

620

370

580

430

715

317,8

54,96

7,04

Experience results for factors of production We take into account the average life span per group of factors, without considering the environmental factors directly.
Dielectric  Production temperature  Durée de vie 
1  1  396,25 
1  2  625 
2  1  505 
2  2  715 
To verify the conditions necessary for an analysis of variance, we must check the independence of the samples, the normality of the distribution and the homogeneity of the variances.
To test the normality of the distribution, we use a ShapiroWilk test. Statistic : 0.984044, Probability: 0,900591 . The probability of the test performed is greater than 5%, we can not reject the idea that the service life follows a normal distribution at the 95% level of confidence. The normality graph confirms the Gaussian distribution.
The plot of residuals by number of observations makes it possible to highlight the independence of the samples.
The plot of Residues by Production Temperature and Dielectric allows to conclude a homogeneous variance. The two graphs show residual variances of the same level.
Analysis with second order interactions.
The Pareto graph shows that the AB interaction is negligible. As part of the study, we will not consider this interaction. Analysis without AB interaction
By eliminating the AB interaction, we can evaluate the quality of each factor in the model. The results are as follows:
Source  Production Sum of squares  DDL  Mean quadratic  Report F  Proba. 
A:Dielectrique  9875,39  1  9875,39  112,36  0,0599 
B:Température Production  48125,4  1  48125,4  547,56  0,0272 
Total Error  87,8906  1  87,8906  
Total (corr.)  58088,7  3 
The effects graph highlights the effect of each of the factors. It highlights and corroborates the analysis of the variance on the strong effect of the production temperature in the model. The effect of the dielectric is less important and can be neglected. The model adjusted with the dielectric factor is as follows: CONSTANT:560,313 , Diélectrique:49,6875 , Température Production:109,688. The equation of the adjusted model is: Durée de vie = 560,313 + 49,6875*Diélectrique + 109,688*Température de Production . The best combination that achieves the longest life is a dielectric factor of type 2 and a production temperature factor of level 2. This brings us to an estimated lifetime of 879.064 hours. The adjusted model without the dielectric factor is as follows: Durée de vie = 231,25 + 219,375*Température de Production. The best combination that achieves the longest life is a production temperature factor of 2. This brings us to an estimated life of 670 hours.
Dielectric  Production temperature  S / B The biggest of the best  S / B Target value 
1  1  49,2  3,85 
1  2  53,3  5,63 
2  1  50,5  3,8 
2  2  54,96  7,04 
The analysis of the values and graphs of the effects makes it possible to choose the best combination respecting the instructions of robustness. Thus, the choice of the type 2 production temperature and the type 2 dielectric appears again as the best compromise.
{" "} Voltage has a preponderant effect on the effect of noise in our model. The temperature factor of the environment is negligible in view of the Pareto graph. This is confirmed by the effects graph. The following variance analysis can also be checked:
Source  Sum of squares  DDL  Mean quadratic  Report F  Proba. 
A:Tension 1  1,38195E6  1  1,38195E6  29,07  0,0000 
B:Tension 2  314028  1  314028  6,61  0,0158 
C:Temperature Environnement  87153,1  1  87153,1  1,83  0,1866 
Total Error  1,33116E6  28  47541,5  
Total (corr.)  3,1143E6  31 
The data used is taken from the previous choice which is the Dielectric factor at Level 2 and the Production temperature factor at level 2.
Tension  Temperature  Lifetime 
200  175  1100 
200  190  1080 
250  175  1080 
250  190  460 
300  175  620 
300  190  370 
350  175  580 
350  190  430 
The analysis of the results allowed us to highlight the best compromise between the robustness and the longer life of surface response capacitors. Thus, it emerges from the foregoing elements, the surface capacitor having a type A2 dielectric and a type B2 production temperature. Based on this choice, we have determined, through a survival data regression model, that the surface response capacitor of this type has an estimated lifetime value of 92763 hours (10.6 years). Combined with the adjusted model graph, we found that the most robust of this type of surface response capacitor exceeded 130,000 hours (14.8 years).